Riddle Me This

Can you believe it? This is my 153rd post on A Ton Of Bricks!

Oh.

Yeah.

I just mentioned this the other day.

Never mind.

Now on to this week's FUN WITH PHYSICS!

So, as I was meandering (side note: the preceding word has it's origins in the name of the Maeander River in Phrygia, which was famed for it's windiness!) the internet, I stumbled across a Random Insult Generator. An example: I'd like to see things from your point of view but I can't seem to get my head that far up my ass. Associated with this generator are several others, including a Random Fact Generator, and a Random Famous Quote Generator. But what really got me thinking was the Random Riddle Generator. The first riddle I got was (and this isn't an exact quote): if you were 8 feet away from a wall and with each step moved half the distance to the wall, how many steps would it take to come in contact with the wall? The answer? It was, of course, a pithy "oh, you'll never get to the wall, but you will be taking some pretty small steps!" Ha ha ha. Oh wow, like I've never heard of Xeno's paradox you stupid internet thingy. But I'm here to tell you that the answer provided is absolutely and unequivocally wrong. That's right, it's wrong.

Let me explain. There is a property of the universe called the planck length (named after, guess who, Max Planck!). This length is the smallest possible distance that makes any sense in the universe. I won't go into the gritty details of it here, though. I'll suffice to say that it is based on the planck mass, which is the mass of a particle with a Compton Length equal to its Schwarzschild radius (which I believe I've mentioned before). When those two lengths are equal, that is the planck length, or about 1.6 x10^-35 meters. Anything smaller than this does not exist, since no information can ever be gleaned from smaller distances (kind of like a mini black hole, but different). Anyway, what this means is that when two things are separated by one planck length, they are actually touching. It has to do with the quantum uncertainty in the position of the particles. Just trust me. Or not. You can read about it on wikipedia, too. When we apply this idea to the riddle, it's a simple calculation to find that, if you start at 8 feet (2.4384 meters) out, after 117 steps you will be within one planck length of the wall, meaning you are actually touching the wall. Now you could also make the argument that at one step prior to that (116 steps), the next step would be physically impossible since it would need to be smaller than one planck length, so that you are actually touching the wall (by that I mean you can get no closer to the wall than you currently are) at a distance of 2.94 x10^-35 meters. Either argument holds water with me, but both say that after just over 100 steps you WILL reach the wall.

Come on riddle writers, learn some physics.

This idea can also apply to Xeno's paradox where you have an arrow moving at a constant speed. There is a unit of time called (guess what!) the planck time that is the smallest meaningful period of time in the universe. It is equal to the amount of time it takes a photon in a vacuum to pass through the planck length: about 5.39 x10^-44 seconds. From there, the argument is analogous and eventually the arrow does come in contact with the target.


This post contain 12 links, 6 of which are nearly incomprehensible physics articles.